Question

Determine if the following side lengths could form a triangle.

Prove your answer with an inequality.

8,17,24

Answer 1

To determine if the given side lengths (8, 17, 24) can form a triangle, we can apply the Triangle Inequality Theorem. According to the theorem, for any triangle with side lengths a, b, and c, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Let's apply this theorem to the given side lengths:

8 + 17 > 24

17 + 24 > 8

8 + 24 > 17

By checking these inequalities, we can see that all three conditions are satisfied. Therefore, the given side lengths of 8, 17, and 24 can form a triangle.